How do you know when to put an open or closed circle when graphing inequalities?
1 answer:
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To graph the line, we must first find out the equation for the line in slope-intercept form (y = mx + b). So far, we only have the slope, so the line's equation is y = 3/4x + b. But, by inserting the values of x and y in the point we know, we can find the y - intercept.
4 = 3/4 + b
b = 13/4
That means that the equation of our line is y = 3/4x + 13/4. Now we can graph. But, there is another way to go about (slightly faster too). Since we know the coordinates of 1 point, we can put that line down. Then, since we know that slope is rise over run, we can say, that with a slope of 3/4, one would go 3 points up for every 4 to the right. Now we can go 3 points up and 4 points to the right of point (1,4). That would be (5, 7). Now we can graph (since we have 2 points, or an equation).
The graph looks like this:
The potential solutions of are 2 and -8.
From the properties of logarithms, you can rewrite logarithmic expressions.
The main properties are:
- Product Rule for Logarithms -
- Quotient Rule for Logarithms -
- Power Rule for Logarithms -
The exercise asks the potential solutions for . In this expression you can apply the Product Rule for Logarithms.
Now you should solve the quadratic equation.
Δ=. Thus, x will be
. Then:
The potential solutions are 2 and -8.
Read more about the properties of logarithms here: